Runaway processes on neutron stars leading to the sudden release of large quantities of energy (up to of order 1040 erg) on time scales as short as a fraction of a second involve plasma heating and particle acceleration in superstrong magnetic fields H (of order 1012 G). These transient events are interesting from a theoretical standpoint because they require knowledge of particle transport properties in low-density plasmas (ne ≲ 1025cm−3) threaded by both electric (E) and magnetic fields. The evaluation of matrix elements involving solutions to the Dirac equation for such a field configuration is often difficult and sometimes impossible, since no completely normalized wave function has yet been found. Here it is shown that, in the special case of E/H ≲ 10−4, a simplification of the overlap integrals permits an analytical integration that yields explicit expressions for the relativistic charge currents needed in the computation of the anisotropic conductivity tensor when E.H ≠ 0. The application of these results to the evaluation of the conductivity is briefly discussed. Among other things, this work is relevant to a theory of resistive magnetic tearing instabilities in a quantizing field.
ASJC Scopus subject areas
- Condensed Matter Physics